Preheat the oven to 400°F (200°C).
Combine the sea salt, garlic powder, black pepper, and Italian seasoning in a small bowl.
Drizzle half of the olive oil over a large rimmed baking sheet, spreading it lightly across the surface.
Pat the chicken dry. Season both sides with part of the prepared seasoning mixture.
Arrange the seasoned chicken pieces on the baking sheet in a single layer.
Add the sliced zucchini, yellow squash, and grape tomatoes around the chicken.
Drizzle the remaining olive oil over the chicken and vegetables.
Sprinkle the remaining seasoning mixture evenly over the vegetables.
Bake the Easy Baked Chicken with Zucchini Recipe for 15–20 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) at its thickest point and the vegetables are fork-tender.
If desired, sprinkle shredded Parmesan over the hot chicken and vegetables before serving.